Lipschitz Estimates for Conformal Maps from the Unit Disk to Convex Domains
Complex Variables
2022-02-25 v2
Abstract
We obtain an explicit uniform upper bound for the derivative of a conformal mapping of the unit disk onto a convex domain. This estimate depends only on the outer and inner radii of the domain, and on a curvature radius of its boundary. Its proof is based on a M\"obius invariant metric of hyperbolic type, introduced by Kulkarni and Pinkall in 1994.
Cite
@article{arxiv.2106.03808,
title = {Lipschitz Estimates for Conformal Maps from the Unit Disk to Convex Domains},
author = {Christopher G. Donohue},
journal= {arXiv preprint arXiv:2106.03808},
year = {2022}
}
Comments
12 pages, 1 figure